How to avoid extraneous edges when using loop cut?
In this specific case, I think think the best thing is to use the cut tool k.

In specific answer to your question, the way to create a loop cut, without having it go all the way down the surface, is ripping an edge v. In your case, you would rip the edge right along the extrusion, and the front edge to the right of it. Then make your loop cuts. You can then mend the edges if you wish, by deleting the extra edge (will remove the face of the wall), adding faces (such as tris, because in the game engine it converts to tris anyway) or by making an n-gon face over the whole section.

I hope this helps. If you give me your blend file I can make examples.